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Kapranov’s $L_\infty$ structures, Fedosov’s star products, and one-loop exact BV quantizations on Kähler manifolds
Communications in Number Theory and Physics ( IF 1.9 ) Pub Date : 2022-04-27 , DOI: 10.4310/cntp.2022.v16.n2.a2
Kwokwai Chan, Naichung Conan Leung, Qin Li

We study quantization schemes on a Kähler manifold and relate several interesting structures. We first construct Fedosov’s star products on a Kähler manifold $X$ as quantizations of Kapranov’s $L_\infty$-algebra structure. Then we investigate the Batalin–Vilkovisky (BV) quantizations associated to these star products. A remarkable feature is that they are all one-loop exact, meaning that the Feynman weights associated to graphs with two or more loops all vanish. This leads to a succinct cochain level formula in de Rham cohomology for the algebraic index.

中文翻译:

Kapranov 的 $L_\infty$ 结构、Fedosov 的星积以及 Kähler 流形上的单环精确 BV 量化

我们研究了 Kähler 流形上的量化方案并关联了几个有趣的结构。我们首先在 Kähler 流形 $X$ 上构造 Fedosov 的星积,作为 Kapranov 的 $L_\infty$-代数结构的量化。然后我们研究与这些明星产品相关的 Batalin-Vilkovisky (BV) 量化。一个显着的特征是它们都是单循环精确的,这意味着与具有两个或更多循环的图相关的费曼权重都消失了。这导致了代数索引的 de Rham 上同调中简洁的 cochain 级别公式。
更新日期:2022-04-27
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